Diophantus & Late Antiquity
The father of algebra and the twilight of Hellenistic scholarship
6.1 Diophantus of Alexandria
Diophantus (c. 200–284 CE) wrote the Arithmetica, a collection of 130 problems (of which about half survive) involving the solution of equations in integers or rational numbers. His work represents a dramatic departure from the geometric tradition of Greek mathematics — it is algebraic in spirit, using abbreviations and symbols to manipulate unknown quantities.
Diophantine equations — polynomial equations where only integer solutions are sought — remain a central topic in modern number theory. Fermat's famous “Last Theorem” was scrawled in the margin of a copy of Diophantus's Arithmetica.
Video Documentary
Watch the documentary on Diophantus in our Video Lectures page — “Before Newton and Einstein There Was Diophantus.”
6.2 Hypatia of Alexandria
Hypatia (c. 360–415 CE) was the last great mathematician of the Alexandrian tradition. The daughter of Theon of Alexandria, she wrote commentaries on Diophantus's Arithmetica and Apollonius's Conics, and was renowned as a teacher and philosopher.
Her murder by a Christian mob in 415 CE is often taken as symbolic of the end of the classical intellectual tradition in Alexandria. The mathematical heritage she helped preserve would survive mainly through Arabic translations.
6.3 The Transmission of Knowledge
As the Roman Empire declined, the Greek mathematical tradition was preserved through two main channels: Byzantine scholars who maintained Greek manuscripts in Constantinople, and Arabic translators who rendered Greek texts into Arabic during the Islamic Golden Age.
Without these preservation efforts, works by Euclid, Archimedes, Apollonius, and Diophantus might have been lost forever. The translation movement centered at the House of Wisdom in Baghdad (founded c. 832 CE) would not only preserve but build upon this heritage, creating new mathematics that eventually flowed back to Europe.